Kinematic source inversions, a statistical approach:

Seismic and geodetic data are frequently used to invert for the spatio-temporal evolution of slip along a rupture plane. It was noted that images of along-fault slip evolution vary distinctly, depending on the adopted inversion approach and rupture model parameterization. Which --if any-- of the provided kinematic models is "correct" and how accurate are fault parameterization and solution predictions? These issues are not included in "standard" source inversion approaches. We aim to address these issues using a statistical inversion approach (as opposed to standard deterministic inversion) by implementing Markov Chain Monte Carlo (MCMC) algorithms and Bayes theorem. Instead of "directly" inverting for a solution (the solution being the space-time along-fault slip distribution) we propose such a solution, generate synthetic seismograms from it and then determine the misfit between observed and synthetic seismograms. MCMC and Bayesian statistics then allow to identify the most probable solution (after proposing a large number of trial solutions), defined by the posterior joint PDF. Any already computed posterior PDF can in turn be considered prior information as soon as new seismic data --or any other auxiliary information-- becomes available. The adopted approach thus allows to continuously update our knowledge about the seismic event as new data is provided. For the sampling from the probability distribution (MCMC), we use a library of functions called QUESO, developed by our collaborator at UT Austin.

Numerical earthquake simulations:

Numerical earthquake simulators--physics-based computer models in which earthquakes may spontaneously occur due to changes in stressing conditions along predefined fault surfaces-- may help to better understand fault behavior, earthquake recurrence, and the potential for earthquake forecast. Thorough parameter space investigations may allow to identify which (if any) of the multiple processes and parameters involved in the rupture process are dominating individual aspects or the overall system behavior. Earthquake simulators also enable to challenge preconceived conceptual knowledge of earthquake behavior: Under what sets of parameters do simulator results correspond to seismic and geologic observations? Are these parameters reasonable?

Although earthquake simulators present a powerful emerging tool, these computer models face a number of potentially severe challenges--similar to simulations in other (earth-)scientific disciplines such as geodynamics, geomorphology, seismology, and volcanology: a) Simulating a multi-dimensional highly complex system of interacting processes, b) Often using only rough estimates for initial and boundary conditions, c) Dealing with an often spatio-temporal heterogeneous parameter distribution, and d) Spatio-temporal simulations-scale is often (significantly) coarser then the process scale. Despite these obstacles, numerical models in earth sciences, including numerical earthquake simulations, may still contribute to a better understanding of the investigated system. When formulated well, these models allow to explore ideas, formulate initial hypothesis of system behavior, and ulceratively to predict i.e., forecast its behavior (mostly in a statistical sense) [Bras et al., 2003].

As part of my dissertation work, I have developed the quasi-static numerical earthquake simulator FIMozFric to investigate earthquake magnitude-frequency relationships, earthquake recurrence models and how they are affected by fault properties such as fault geometric roughness (a proxy for fault maturity). FIMozFric is build on analytical expressions for internal displacement and strains due to slip along rectangular faults [Okada, 1992]. The key aspects ofFIMozFric model formulation are schematically represented in the figure to the right (top). Also shown are example along-fault slip distribution for partial rupture and full rupture earthquake(s). I am currently working on an number of model improvements including the transition from rectangular to triangular fault patches (better representation of rough surfaces), implementation of a slip-weakening friction law with depth-dependent weakening behavior, and parallelization of the simulator (allows simulation of significantly larger fault systems i.e., better spatial resolution). I'm also contemplating including some approximation for visco-elastic behavior of the aseismic crust -doing so is likely to allow generation of aftershock sequences.

Earthquake recurrence models:

Earthquake recurrence models such as the ones presented to the right [Schwartz and Coppersmith, 1984] summarize the current conceptual knowledge of how earthquake slip accumulates along individual faults. While more recent models which also include temporal clustering have been proposed [e.g., Friedrich et al., 2003], the model(s) presented by Schwartz and Coppersmith [1984] are still dominating the current view on earthquake recurrence. Knowing which of these (or other) models presents the best approximation of actual fault behavior and understanding why different faults are better represented by different recurrence models is of great importance in seismic hazard analysis and the overall understanding of fault behavior. Those recurrence models are based on geologic observations, namely paleoseismic and tectono-geomorphic studies. Data density (particularly the spacing of paleoseismic sites) is generally low, limiting the reliability of event correlation between those sites. Emergence of freely available LiDAR data (www.opentopography.org) provides an additional tool to investigate along-fault slip distributions.

As part of my dissertation work, I used the "B4" LiDAR data for the south-central San Andreas Fault (SAF) to reconstruct the along-fault surface slip distribution of the great 1857 Fort Tejon (Mw7.9) and preceding major earthquakes. For this study I developed the MATLAB-based GUI LaDiCaoz that enables fast and easy-to-reproduce offset measurements.

I am interested in better understanding how slip along a fault recurs, how this recurrence pattern varies along the fault and how it is affected by fault geometric properties (i.e., how it varies from fault to fault and within an interacting fault system): Fault geometry will certainly affect those recurrence patterns as it controls whether multi-fault (segment) rupture may occur and how frequent it is. Besides field-based studies (paleoseismic excavations and measurements of tectonically offset geomorphic markers, I use numerical earthquake simulations to investigate this topic.

Earthquake magnitude-frequency relationships:

While it is widely accepted and observed that the earthquake magnitude-frequency relationship (MFR) for global seismicity is well described by an inverse power-law relationship known as the Gutenberg-Richter (GR) relation, a number of data sets [e.g., Wesnousky, 1994; Knopoff, 2000; Ben-Zion, 2003] suggest that MFR on regional scale or for individual faults may be better described by a characteristic (i.e., bimodal) MFR. The latter refer to the observation for individual faults (pronounced for long and spatially isolated faults) that small to moderate size earthquakes along it follow the GR while large earthquakes occur more frequent than anticipated from GR, forming a secondary peak in earthquake probability (thus creating bimodal behavior). Whether seismic behavior of single faults is better described by GR or by characteristic i.e., bimodal earthquake model (CEM and BEM respectively) is still unresolved. A main problem in this case is the general lack of complete seismic records for single faults that span multiple earthquake cycles (Parkfield, CA being one of few exceptions).

As part of my dissertation work, I have used the numerical earthquake simulator FIMozFric to investigate MFR of single, spatially isolated faults of different fault geometric complexity. These and further earthquake simulations suggest that seismic behavior may change over geologic time scales as the fault becomes more mature and structural complexity decreases. Based on these simulations, seismic behavior evolves gradually from GR to BEM behavior as the respective fault becomes increasingly smooth.

However, simulations alone certainly cannot solve this important outstanding problem. Geologic and seismologic observation with high spatial and temporal resolution are also required. I am interested in working with those observational data to confirm or discard the suggested working hypothesis of an evolution from GR to BEM as a fault matures. I am furthermore interested in determining to what degree fault system interactions affect fault behavior and MFR of individual structures.

The great 1857 Fort Tejon earthquake along the SAF, CA:

The great 1857 Fort Tejon earthquake (Mw7.9) with a rupture length of ~350km is the most recent major earthquake along the south-central San Andreas Fault (SAF). Previous surface-slip reconstructions of the 1857 [e.g., Sieh, 1978; Sieh and Jahns, 1984; Schwartz and Coppersmith, 1984] and preceding major events along its surface rupture trace have been a cornerstone in shaping current perception of fault behavior, fault segmentation, and earthquake recurrence models. As part of my dissertation work I used the "B4" LiDAR data set to essentially repeat the previous studies and measure the surface slip distribution along the 1857 rupture trace. Repetition is largely justified by the exceptional spatial resolution of the "B4" data set, enabling identification of even subtle geomorphic features. Overall, the new measurements correlate well with previous observations. However, the number of identified offset features and therefore data density increased significantly: by a factor of 2-3. While reconstruction of the 1857 event was relatively simple, reconstruction of previous events proved to be distinctively more difficult and less reliable.

I am interested in understanding and studying the slip history of the southern SAF as it presents an example for fault behavior of a structurally mature fault. I am interested in reconstructing the surface slip distribution of large earthquakes that precede the 1857 event. I am also interested in comparing its behavior with the behavior of other faults in similar of lower fault evolutionary stages. Do slip accumulation patterns change systematically as a function of fault evolutionary stage i.e., fault geometric complexity? How is behavior (slip accumulation) affected by fault interaction? The SAF, particularly the Carrizo Plain section effectively presents an end member case where the fault is very mature and spatially isolated.

Paleoseismicity along the SAF, CA (Bidart Fan site):

In recent years the Bidart Fan site in the Carrizo Plain along the San Andreas Fault (SAF) has become increasingly important in constraining the event history of the south-central SAF as it provides reasonably well preserved stratigraphy as well as (relatively) abundant datable material (for radio-carbon dating). This site therefore provides the opportunity to constrain event ages as well as the associated offsets. Together with Lisa Grant Ludwig, Ramon Arrowsmith, and Sinan Akciz I have been part of the paleoseismic investigations at this site from 2005 to 2009. The LiDAR based hillshade map to the right presents the outlines of all trench locations that have been excavated over the years (note that two of them have been excavated by Lisa Grant in the 1990s).

I am interested in further constraining the slip history at this site and other locations along the south-central SAF (the Carrizo Plain in particular) as it allows to test previously defined conceptual models of fault behavior, fault segmentation and earthquake recurrence. Besides narrowing down the error bars on slip-per-event and event timing at known sites, it is important to explore additional sites to increase data density and therefore reliability of slip history reconstruction.

Paleoseismicity along the Marmanet escarpment, Subukia valley, Kenya:

The seismicity of the Kenya rift, East Africa, is characterized by high-frequency, low-magnitude events concentrated along the rift axis. Its seismic character is typical for magmatically active continental rifts, where igneous material at a shallow depth causes extensive grid faulting and geothermal activity. Thermal overprinting and dike intrusion prohibit the buildup of large elastic strains, therefore prohibiting the generation of large-magnitude earthquakes. On 6 January 1928, the Ms 6.9 Subukia earthquake occurred on the Laikipia–Marmanet fault, the eastern rift-bounding structure of the central Kenya rift. With a ~40km long surface rupture and a maximum vertical throw of 2.4m (average throw was reported as 1m), it is the largest instrumentally recorded seismic event in the Kenya rift, standing in contrast to the just mentioned current model of the rift’s seismic character in which large earthquakes are not anticipated. Detailed reports on the historical accounts of these events were published by Richter [1958], McCall [1967], and Ambraseys [1991]. While local accounts suggest that earthquake activity is common in this region, the seismic character of the Laikipia-Marmanet Fault (timing and size of EQs preceding the 1928 rupture) is not well known.

I had the opportunity to conduct a paleoseismic excavation along the Laikipia-Marmanet Fault, Subukia Valley, Kenya, excavating a section of the 1928 surface rupture trace. This excavation was part of my Diplom thesis research supervised by Manfred Strecker and Anke Friedrich. We identified stratigraphic evidence for six surface-rupturing earthquakes with a total vertical throw of ~7.5m. Due to the poor quality of the radiocarbon samples, we were not able to bracket the ages of these events but estimated the scarp age via scarp diffusion modeling.

One reason for my continued interest in this earthquake and fault system is it stands in contrast to the current model of the rift’s seismic character in which large earthquakes are not anticipated: the rift-bounding structure that ruptured in 1928 remains seismically active, capable of generating large-magnitude earthquakes, even though thermally weakened crust and better oriented structures are present along the rift axis nearby, prohibiting any significant buildup of elastic strain. This observations implies that crustal deformation is not narrowly concentrated along the rift axis but more diffuse.